Question

The reaction of hydrogen and oxygen gases produces \(15.0 \mathrm{~g}\) of water and releases 48.0 kcal of heat. How much energy is required to decompose \(15.0 \mathrm{~g}\) of water into hydrogen and oxygen gases?

Short answer

48.0 kcal of energy is required to decompose 15.0 g of water.

Step-by-step solution

Understanding the Reaction

The reaction given involves hydrogen and oxygen gases combining to form water while releasing 48.0 kcal of heat. This is an exothermic reaction, meaning that energy is released when the reaction occurs.

Concept of Energy in Reactions

For a chemical reaction, the energy required to decompose a compound is equivalent to the energy released when it was formed, but the sign is opposite. So, the energy needed to decompose water into hydrogen and oxygen is equal in magnitude to the energy released during its formation.

Calculation of Required Energy

Since the formation of 15.0 g of water releases 48.0 kcal, the decomposition of the same amount of water will require 48.0 kcal of energy. This is because in chemical reactions, the energy involved is conserved and will just change sign based on the direction of the reaction.

Key concepts

Exothermic Reactions

In chemistry, exothermic reactions hold a key role because they **release energy** in the form of heat. When a reaction is exothermic, it means energy is being discharged from the system into its surroundings. A practical example of an exothermic reaction is the combination of hydrogen and oxygen gases to form water.
\[ \text{H}_2 (g) + \frac{1}{2}\text{O}_2 (g) \rightarrow \text{H}_2\text{O} (l) + \text{energy (heat)} \]
Understanding that energy is released can help explain why such reactions often occur spontaneously. Think about lighting a match; once the flame starts, it releases energy without needing further help.
Exothermic reactions are vital in both natural processes and industrial applications, such as combustion engines and energy production in power plants. The key idea is that the products formed have less stored energy than the reactants, with the difference being released as heat. This characteristic of releasing energy distinguishes exothermic reactions from their endothermic counterparts.

Energy Conservation in Chemical Reactions

In chemical reactions, the principle of energy conservation is crucial. This principle states that energy cannot be created or destroyed, only transformed or transferred. This is especially evident when observing reactions such as the formation and decomposition of water.
When hydrogen and oxygen gases come together to form water, energy is released - this is captured by the term 'release of 48.0 kcal of heat.'
On the flip side, if we want to decompose that same amount of water back into hydrogen and oxygen gases, the same amount of energy, 48.0 kcal, is required, representing the energy stored in the bonds.
Here's a simplified view:

• **Energy released** during formation = **Energy absorbed** during decomposition.
• This demonstrates the conservation of energy: \( \text{Energy in} = \text{Energy out} \).

Thus, in our original exercise, the 48.0 kcal released when forming water would need to be supplied again for decomposition, highlighting how energy conservation works in reversible reactions.

Decomposition Reactions

Decomposition reactions are a type of reaction where a single compound breaks down into two or more smaller substances. In contexts like our exercise, decomposition reactions require an input of energy because they involve breaking bonds, which inherently consumes energy.
The decomposition of water is represented by:\[\text{H}_2\text{O} (l) + \text{energy} \rightarrow \text{H}_2 (g) + \frac{1}{2}\text{O}_2 (g)\]This process is the reverse of an exothermic reaction and is known as an **endothermic reaction**, where energy must be absorbed for the reaction to proceed. Decomposition reactions can be initiated by heating, applying electricity, or increasing pressure, depending on the compound.
• **Thermal decomposition**: Heat is used to break chemical bonds.• **Electrolytic decomposition**: Electricity acts as the energy source, as seen in water electrolysis.
Understanding decomposition reactions not only helps in predicting reaction behaviors but is essential for industrial processes like the production of gases and other materials from compounds. Through decomposition, chemists can isolate and use elements in various applications, embodying a cornerstone of chemical manufacturing and analysis.